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DieHenkels (talk | contribs) m →Exchange functional: formula in SI units added |
DieHenkels (talk | contribs) m →Correlation functional: Si units restored in formula for Wigner-Seitz r_s |
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:<math>\epsilon_{\rm c} = \frac{1}{2}\left(\frac{g_{0}}{r_{\rm s}} + \frac{g_{1}}{r_{\rm s}^{3/2}} + \dots\right)\ ,</math>
where the [[Wigner–Seitz cell|Wigner-Seitz parameter]] <math>r_{\rm s}</math> is dimensionless.<ref name="Murray Gell-Mann and Keith A. Brueckner 1957 364">{{cite journal | title = Correlation Energy of an Electron Gas at High Density | author = Murray Gell-Mann and Keith A. Brueckner | journal = Phys. Rev. | volume = 106 | pages = 364–368 | year = 1957 | doi = 10.1103/PhysRev.106.364 | issue = 2| bibcode = 1957PhRv..106..364G | s2cid = 120701027 | url = https://authors.library.caltech.edu/3713/1/GELpr57b.pdf }}</ref> It is defined as the radius of a sphere which encompasses exactly one electron, divided by the Bohr radius
:<math>\frac{4}{3}\pi r_{\rm s}^{3} = \frac{1}{\rho \, a_0^3}\ .</math>
An analytical expression for the full range of densities has been proposed based on the many-body perturbation theory. The calculated correlation energies are in agreement with the results from [[quantum Monte Carlo]] simulation to within 2 milli-Hartree.
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